The M-bootstrap estimation of heavy-tailed index and empirical analysis of Chinese stock markets

Estimating the tail index of a heavy-tailed distribution depends on the choice of the number k of upper order statistics used in the estimation. In this paper, we reviewed estimating tail index of the heavy-tailed distribution historic course. We summarized selecting k from the heavy-tailed index to the research state and discussed the sum-plot method and bootstrap method of selecting k from heavy-tailed index estimating in detail. And improved the bootstrap method which proposed by Hall, which is called the M-bootstrap method. And we used the above three methods to carry on the Monte-Carlo simulation to the known heavy-tailed distribution, studied their feasibility, compared them with their robust. The results of these three methods are satisfied. Sum-plot method and M-bootstrap method arenpsilat impacted by outliers. Afterwards we made empirical analysis based on Shanghai Stock Index and Shenzhen Component Index data, the computed result indicated that Shanghai Stock Index and Shenzhen Component Index returns ratio is thick-tailed and expose right skew, right tail heavier on left tail.